I am thinking of retiring in Taiwan; what sort of investment do I need to consider for retirement overseas?

You may want to buy a property in Taiwan since you need a roof over your head during your retirement. Moreover, it is better to be a landlord than to be a tenant since you can collect rental. However, you need to read up Taiwan housing and tax regulations. Your portfolio may or may not need to have Taiwanese stocks as long as you have a diversified portfolio with different assets classes with different correlations. Just my humble opinion.

No you do not need to hold Taiwan stocks to retire there. Remain globally diversified.

Your main concern would be currency hedging, coningency plans if you ever need to return to Singapore, and healthcare and insurance for your time in another country.

As long as your portfolio generates streams of guaranteed income and adjusts for inflation, you should be fine.